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"To them, I said, the truth would be literally nothing but the shadows of the images."
- Plato: The Allegory of the Cave
"Achilles: Was it (a sound record) a present for the Crab?
"Tortoise: Absolutely! I suggested that we listen to it on his new phonograph ... So he put it on. But, unfortunately, after only a few notes, the record player began vibrating rather severely, and then with a loud "pop", broke into a large number of fairly small pieces, scattered all about the room."
- Dialog Contracrostipunctus in "GEB" by Douglas Hofstadter
Mass-spring system and Hooke's Law. Concept of restoring force.
Vibrating motion. Period and frequency of vibrations.
Pendulum. Conservation of energy in mass-spring system and pendulum. Speed as a function of position.
Reference circle. Motion of a shadow and its similarity to mass-spring system and pendulum.
Simple harmonic motion (SHM). Periods of vibrations for the mass-spring system and pendulum.
Plato's "Allegory of the Cave".
Equations for displacement/position and velocity in SHM. Solutions of the differential equation of SHM. Amplitude and phase.
Damped oscillations.
Vibrations under influence of external periodic force. The phenomenon of resonance. Resonant frequency.
Presentation: Description of Oscillatory Motion
Presentation: Description of Oscillatory Motion
Presentation: Spectra, Damped Vibrations and Resonance Phenomenon
Presentation: Spectra, Damped Vibrations and Resonance Phenomenon
Practice Assignments:
Practice Assignments:
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